Understanding Velocity of Balls Thrown Upward and Downward

Two students are on a balcony a distance h above the street. One student throws a ball vertically downward at a speed vi; at the same time, the other student throws a ball vertically upward at the same speed.

Answer the following symbolically in terms of vi, g, h, and t. (Take upward to be the positive direction.)

Use the time-independent kinematics equation to find the velocity of each ball as it strikes the ground.

Final Answer:
The velocity of the ball thrown downward when it strikes the ground is given by:
v_down = vi + gt
The velocity of the ball thrown upward when it strikes the ground is given by:
v_up = vi - gt

Explanation:
When one student throws a ball downward and the other upward, we can use time-independent kinematics equations to find the velocities of the balls as they strike the ground. For the ball thrown downward, its initial velocity is vi and it is subject to the acceleration due to gravity g. Using the equation v_down = vi + gt, we find that its velocity as it strikes the ground is v_down.
For the ball thrown upward, it also has an initial velocity of vi but in the opposite direction to gravity. So, its acceleration is -g. Using the same equation, v_up = vi - gt, we find that its velocity as it strikes the ground is v_up.
In both equations, t represents the time it takes for the balls to strike the ground. In summary, the first ball thrown downward gains speed due to gravity, while the second ball thrown upward loses speed due to gravity. This results in the two different final velocities when they hit the ground.